IB Physics Experiment: Nerf Dart Projectile Motion

Research Question

What is projectile motion?

Hypothesis

Even when the Nerf gun is placed horizontally to the target and aimed at the target’s bullseye with pinpoint accuracy, the dart will not hit the bullseye when shot. Instead the dart will hit the target lower than the aimed spot or even not reach the target at all.

Theoretical Background

Projectile motion is a form of motion a projectile (object) does when it is thrown near the earth’s surface, making it move in a parabolic path (trajectory). Projectile motion happens when a force is applied at the beginning of the trajectory (ex: throwing a ball), and then the projectile motion happens when gravity interferes with it and pulling it down.

Variables

Independent Variable : Angle of the Nerf gun

Dependent Variable : Accuracy of the dart

Controlled Variable : Nerf gun position

Materials & Equipment

Nerf pistol (and darts)

Meter stick

Long measuring tape

Large protractor

Long string

Marker (mark spots)

Procedures

Finding muzzle velocity

Set up Nerf gun 160cm off the ground and 90 degrees horizontal

Shoot

Measure the distance the bullet traveled from the tip of the bullet in the gun to where the bullet hits the ground.

Repeat the steps for five more times and calculate the average distance

From the average distance, calculate the duration or time of the dart falling until it hitting the ground using the equation

t = time, h = distance (160cm), g = gravity (9.81)

Use the time taken and the average distance to find the muzzle velocity by using this equation

Finding the angle to shoot to hit the target

Set up Nerf gun 160cm off the ground and 90 degrees horizontal

Set up the string horizontally so that it will be straight and also 160cm off the ground (this is going to be the target and the benchmark of it being straight or not)

Shoot

Mark where the the bullet hits the target

Adjust the Nerf gun’s angle without changing the position of the Nerf gun

Shoot

Repeat the last two steps until you can hit the target and record the angle.

Data

Data for muzzle velocity:

Dart Trials

Distance in Meters

1

2.6416

2

3.4163

3

3.5179

4

3.302

5

3.2004

6

3.3655

Average

3.24061666582 Meters

Time for the dart to fall 1.6 meters: 0.813 seconds

Muzzle velocity of the Nerf dart: V = 3.986 m/s

Data for finding the angle:

83 Degrees is the angle needed for the dart to hit the target

Analysis

From the data received above, we can find the muzzle velocity of the Nerf to be about 3.986m/s by using the formula stated above. Also from the photo taken above, even though the Nerf gun is placed horizontally 90 degrees to the target and is aimed exactly to accurate to the point of the target, it doesn’t hit the target at all (the average dart trajectory is marked by the marker on the right side of the picture). The Nerf instead goes underneath the target by a big distance. Then after adjusting five degrees, higher than the target, it starts to go nearer to the target. After adjusting more, I found that it is about 83 degrees for the angle needed to hit the target.

Conclusion

The data shown above clearly proves the hypothesis to be true which that even though the Nerf gun is placed horizontally 90 degrees to the target and is aimed exactly to accurate to the point of the target, it doesn’t hit the target at all. This experiment could be improved to show a more accurate result by using better equipment and by using a room that is more controlled. The equipment that should be improved is the Nerf gun itself because the gun is not that consistent in the shooting results, getting mixed results and sometimes the dart just doesn’t go out of the Nerf. Also to improve the results of the experiment, I need a room without the air conditioner affecting the dart trajectory.